question_answer

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are\[{{\text{K}}_{\text{A}}}\], \[{{\text{K}}_{\text{B}}}\] and\[{{\text{K}}_{\text{C}}}\], respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure. Then [NEET - 2018]

A) \[{{\text{K}}_{\text{B}}}\text{}{{\text{K}}_{\text{A}}}\text{}{{\text{K}}_{\text{C}}}\]

B) \[{{\text{K}}_{\text{A}}}\text{}{{\text{K}}_{\text{B}}}\text{}{{\text{K}}_{\text{C}}}\]

C) \[{{\text{K}}_{\text{A}}}\text{}{{\text{K}}_{\text{B}}}\text{}{{\text{K}}_{\text{C}}}\]

D) \[{{\text{K}}_{\text{B}}}\text{}{{\text{K}}_{\text{A}}}\text{}{{\text{K}}_{\text{C}}}\]

Correct Answer: B

Solution :

[b]

Point A is perihelion and C is aphelion.

So, \[{{\text{V}}_{\text{A}}}\text{}{{\text{V}}_{\text{B}}}\text{}{{\text{V}}_{\text{C}}}\]

So, \[{{\text{K}}_{\text{A}}}\text{}{{\text{K}}_{\text{B}}}\text{}{{\text{K}}_{\text{C}}}\]